There is a uniform magnetic field $B$ normal to the $xy$ plane. $A$ conductor $ABC$ has length $AB = l_1$,parallel to the $x$-axis,and length $BC = l_2$,parallel to the $y$-axis. $ABC$ moves in the $xy$ plane with velocity $\vec{v} = v_x \hat{i} + v_y \hat{j}$. The potential difference between $A$ and $C$ is proportional to

$A$ $2 \; m$ wire is moving with a velocity of $1 \; m/s$ perpendicular to a magnetic field of $0.5 \; Wb/m^2$. The induced e.m.f. in it will be $... \; V$.

$A$ horizontal wire of mass $m$,length $l$,and resistance $R$ is sliding on vertical rails in a uniform magnetic field $B$ directed perpendicularly. The terminal speed of the wire as it falls under the force of gravity is ($g =$ acceleration due to gravity).

An infinitely long straight wire carrying current $I$,an open rectangular loop,and a conductor $C$ with a sliding connector are located in the same plane,as shown in the figure. The connector has length $l$ and resistance $R$. It slides to the right with a velocity $v$. The resistance of the conductor and the self-inductance of the loop are negligible. The induced current in the loop,as a function of separation $r$ between the connector and the straight wire,is:

The loop shown moves with a constant velocity $V$ in a uniform magnetic field of magnetic induction $B$ directed into the paper. The potential difference between $P$ and $Q$ is:

$A$ circular coil of radius $30 \ cm$,having $1$ turn and a resistance of ${\pi ^2} \ \Omega$,is placed in a magnetic field of $10^{-2} \ T$. The coil rotates about its diameter with a speed of $200 \ rpm$ in a direction perpendicular to the magnetic field. The value of the induced $AC$ current in the coil will be . . . . . . $mA$.